Geometric Transformation in Digital Image Processing

Applying geometric transformation to bitmapped images is somewhat different since we have to transform every pixel, and this will often require the image is to be resampled. The scale operator performs a geometric transformation which can be used to shrink or zoom the size of an image. Image reduction is commonly known as subsampling.

It is performed in two ways, one is the replacement method where a one-pixel value within a local neighbourhood is chosen to be representative of its surroundings. This method is computationally simple but can lead to poor results if the sampling neighbourhoods are too large. The other method interpolates between pixel values within a neighbourhood by taking a statistical sample of the local intensity values.

An image can be zoomed either through pixel replication or interpolation. The above figure shows how pixel replication simply replaces each original image pixel with a group of pixels with the same value. Alternatively, interpolation of the values of neighbouring pixels in the original image can be performed to replace each pixel with an expanded group of pixels. Most implementations offer the option of increasing the actual dimensions of the original image.